On the number line, a bug p is moving in the positive direction from the point 0, and a bug n is moving in the negative direction from the point 0. the speeds of both bugs are constant. both leave 0 at the same time, and four seconds later p has reached 12 and n has reached –8.if x is the point reached by p after t seconds, and y is the point reached by n after t seconds, express x and y in terms of t.30 seconds after leaving point 0, how far apart are p and n? when will p and n be 300 units apart?

x = 3t and y = 2t

The distance between P and N after 30 seconds is 150 units

P and N will be 300 units apart after 60 seconds

Step-by-step explanation:

∵ The bugs moved with constant speeds

∵ Speed = Distance ÷ Time

∵ Bug P moved 12 units in 4 sec.

∴ Its speed = 12 ÷ 4 = 3 units/sec.

∵ Bug N moved 8 units in 4 sec.

∴ Its speed = 8 ÷ 4 = 2 units/sec.

∵ P reached point x after t seconds

∴ x = 3t

∵ N reached point y after t seconds

∴ y = 2t

∵ t = 30 sec.

∴ x = 3 × 30 = 90 units

∴ y = 2 × 30 = 60 units

∴ The distance between x and y = 90 + 60 = 150 units

∵ The distance between x and y = 300 units

∴ 3t + 2t = 300

∴ 5t = 300

∴ t = 300 ÷ 5 = 60 sec.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: